Collective Behavior of Heterogeneous Agents in Uncertain Cooperation–Competition Networks: A Nussbaum-Type Function Based Approach

The collective behavior problem is addressed in this article for heterogeneous multiagent systems in uncertain cooperation-competition networks. Here, the agents are described by second-order systems with different velocity damping terms, and the uncertainty of the network is characterized by two unknown nonzero parameters for each agent. Thus, the considered multiagent system can be employed to model the agent network with four kinds of relationships among agents: cooperative relationship and three different competitive relationships. To achieve the desired collective behaviors, a novel distributed Nussbaum-type adaptive controller is designed for each agent. With the help of Barbalat's lemma, it is proved that bipartite consensus can be asymptotically achieved, provided that the weighted network is structurally balanced and connected and that the velocity damping coefficients are chosen appropriately. It is further shown that distributed stabilization can also be asymptotically achieved for the case that the positive weighted subnetwork is connected and some suitable conditions are satisfied. Finally, two illustrative examples are presented to demonstrate the effectiveness of the derived analytical results.